使用 tikz 重新创建图表

Question

我想用 TikZ 重新创建以下图表

借助本网站和 pgfmanual 上针对不同问题的答案，这是我的 MWE

\documentclass[tikz]{standalone}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}[every pin edge/.style={black,thin}, pin distance=7mm]
    \begin{axis}[ 
            xtick=\empty,
            ytick=\empty,
            axis lines =middle, xlabel=$x$, ylabel=$y$,
            every axis x label/.style={at=(current axis.right of origin),anchor=west}
          ]

       \pgfplotsinvokeforeach{-3,-2,...,2,3}{
         \ifnum #1 = -2
           \addplot [blue, smooth,domain=-2:2] {x^2*#1} coordinate[pos=0.68] (n#1);
         \else
           \addplot [blue, smooth,domain=-2:2] {x^2*#1} coordinate[pos=0.64-0.02*#1] (n#1);
         \fi
         \node[inner sep=1pt,pin={[anchor=west]30:$y=#1x^2$}] at (n#1) {};
        }

\addplot [blue,domain=0:360,dashed] ({.5*cos(x)},{.5*sin(x)});
\addplot [blue,domain=0:360,dashed] ({cos(x)},{sin(x)});
\addplot [blue,domain=0:360,dashed] ({1.5*cos(x)},{1.5*sin(x)});
   \end{axis}
\end{tikzpicture}
\end{document}  

和

\documentclass[border=4mm]{standalone}
\usepackage{amsmath}
\usepackage{pgfplots}
\usetikzlibrary{arrows,calc,decorations.pathreplacing}
\pgfplotsset{compat=newest}

\begin{document} 

\begin{tikzpicture}[%
        decoration = {brace,
        amplitude=6pt}]

\tikzset{arrowheads/.style={<->, >=stealth}}
\tikzset{ind arrow/.style={->, blue, bend left=-30, opacity=0.4}}


\draw [->] (-4,0) -- (3.5,0) node [right] {$x$};
\draw [->] (0,-4) -- (0,3.5) node [above] {$y$};
\draw (0,0) circle (1cm);
\draw (0,0) circle (1.7cm);
\draw (0,0) circle (3cm);

\draw [dashed,color=blue,domain = -1.7:1.8] plot(\x, {-1*\x});
\draw [dashed,color=blue,domain = -1.7:1.8] plot(\x, {1*\x});
\draw [dashed,color=blue,domain = -1.7:1.8] plot(\x, {2*\x});

\draw [color=blue, fill=blue] (.8,.6) circle (0pt) node (T){};
\node (Q)[above=.5in,right of=T]{};
\node (R)[right of=Q]{};
\node (P) [blue, above right of=R, align=center] {};

\draw [ind arrow, out=-30, in=180] (P.south east) node[right] {$x^2+\frac12y^2=1$} to (T);
\end{tikzpicture}

\end{document} 

任何改进都值得赞赏！

Answer 1

这看起来让人想起了你的屏幕截图。它假设你想把椭圆画成图，而不仅仅是椭圆，第二个把圆画成圆，而不是图。我使用了一个axis equal符合描述的参数化。（我还根据 minhthien_2016 的建议改进了公式）。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{calc}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16,width=10cm,}
\tikzset{connect with angle/.style={to path={%
let \p1=(\tikztostart),\p2=(\tikztotarget),
\n1={sin(#1-atan2(\y2-\y1,\x2-\x1))} in 
-- ++({(\y2-\y1)*cot(#1)},{\y2-\y1}) -- (\tikztotarget)
}}}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[axis equal,clip=false,
            xtick=\empty,
            ytick=\empty,
            axis lines =middle, xlabel=$x$, ylabel=$y$,
            every axis x label/.style={at=(current axis.right of origin),anchor=west}
          ]

    \pgfplotsinvokeforeach{-3,-2,...,2,3}{
     \ifnum #1 = 0
       \addplot [blue, smooth,domain=-2.5:2.5] {#1*x^2} coordinate[pos={0.2}] (n#1);
     \else
       \addplot [blue, smooth,domain={-sqrt(2.5/abs(#1))}:{sqrt(2.5/abs(#1))}] {#1*x^2} 
       coordinate[pos=0.45-0.12*abs(#1)] (n#1);
     \node[inner sep=1pt,anchor=east,] (nn#1) at ([xshift=1cm]current axis.west|-n#1) 
     {$y=\ifnum#1=1
     \else 
     \ifnum#1=-1
     -\else
     #1
     \fi\fi x^2$};
     \draw[-latex,thin] (nn#1) -- (n#1);
     \fi
    }
   \addplot [blue,domain=0:360,dashed] ({.5*sqrt(2)*cos(x)},{.5*sin(x)})
   coordinate[pos=0.95] (e0);
   \addplot [blue,domain=0:360,dashed] ({sqrt(2)*cos(x)},{sin(x)})
   coordinate[pos=0.05] (e1);
   \addplot [blue,domain=0:360,dashed] ({1.5*sqrt(2)*cos(x)},{1.5*sin(x)})
   coordinate[pos=0.1] (e2);
   \path ([yshift=-2mm]current axis.east|-e0)  node (ne0) {$y^2+\frac{1}{2}x^2=0.5$}
   ([yshift=2mm]e1-|current axis.east)  node  (ne1){$y^2+\frac{1}{2}x^2=1$}
   ([yshift=2mm]e2-|current axis.east)  node  (ne2) {$y^2+\frac{1}{2}x^2=1.5$};
 \end{axis}
   \foreach \X in {0,1,2}
   {\draw[latex-,thin] (e\X) to[connect with angle={-10+30*sign(\X)}]  (ne\X.west);}
\end{tikzpicture}

\begin{tikzpicture}
  \draw [-stealth] (-4,0) -- (3.5,0) node [right] {$x$};
  \draw [-stealth] (0,-4) -- (0,3.5) node [above] {$y$};
  \foreach \X in {1,2,4}
  {\draw (0,0) circle[radius={sqrt(\X)*1cm}] (10:{sqrt(\X)})coordinate (c\X);}
  \draw [dashed,blue] (-3.5,-3.5) -- (3.5,3.5) coordinate[pos=0.9] (x2)
   (-3.5,3.5) -- (3.5,-3.5) coordinate[pos=0.05] (x1)
   (-4/2,-4) -- (4/2,4) coordinate[pos=0.95] (x3);
  \draw[latex-,thin] (x1) -- ++ (-0.5,0) node[left]{$y=-x$};
  \draw[latex-,thin] (x2) -- ++ (0.5,0) node[right]{$y=x$};
  \draw[latex-,thin] (x3) -- ++ (0.5,0) node[right]{$y=2x$};
  \path (4,0.6) node[right] (r4) {$y^2+x^2=4$};
  \path (4,1.2) node[right] (r2){$y^2+x^2=2$};
  \path (4,1.8) node[right] (r1) {$y^2+x^2=1$};
     \foreach \X in {1,2,4}
     {\draw[latex-,thin] (c\X) to[connect with angle={40-\X*5}]  (r\X.west);}
\end{tikzpicture}

\end{document}